[Math] Reference request: Moduli spaces of bundles over singular curves

Question

I would like to know some reference (articles, books…) about any kind of moduli spaces of any of the following objects:

• vector bundles

• torsion-free sheaves

• principal bundles

• parabolic bundles

over singular algebraic curves (reducible or not), in any of the following frameworks:

• algebraic geometry (in characteristic zero and in positive characteristic)

• holomorphic geometry

• integrable systems

• gauge theory

• differential geometry

• topology

• …anything you like…

I would be particularly glad to have some reference about torsion-free sheaves in the algebro-geometric setting.

Thanks

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Edit: I should emphasize that my reference request is about some structures over singular curves. The freedom I expect in a typical answer should be on the structure (e.g. bundles, torsion-free sheaves,…) and on the viewpoint (e.g. pure algebraic geometry, trascendental methods, …), but the base curve must be singular (for the answer not to be offtopic).

Answer 1

Some of the many (semi)standard references are below (with no claims to completeness or representativeness, if that's a word -- just the first references that came to mind). My feeling is the subject is still very much in its infancy however, for example one would like to know the standard package of nonabelian Hodge theory results for singular curves (geometry of Higgs bundles and local systems, Hitchin fibration, its self-duality etc) and there are partial results but no complete picture as far as I know.

Caporaso, Lucia A compactification of the universal Picard variety over the moduli space of stable curves. J. Amer. Math. Soc. 7 (1994), no. 3, 589--660.

Pandharipande, Rahul A compactification over $\overline {M}_g$ of the universal moduli space of slope-semistable vector bundles. J. Amer. Math. Soc. 9 (1996), no. 2, 425--471.

Seshadri, C. S. Moduli spaces of torsion free sheaves on nodal curves and generalisations. I. Moduli spaces and vector bundles, 484--505, London Math. Soc. Lecture Note Ser., 359, Cambridge Univ. Press, Cambridge, 2009. (and earlier papers of his)

arXiv:1001.3868 Title: Autoduality of compactified Jacobians for curves with plane singularities Authors: D.Arinkin

--see this reference for refs to the vast literature by Altman-Kleiman and Esteves-Kleiman on compactified Jacobians

Kausz, Ivan A Gieseker type degeneration of moduli stacks of vector bundles on curves. Trans. Amer. Math. Soc. 357 (2005), no. 12, 4897--4955 (electronic).

Schmitt, Alexander H. W. Singular principal $G$-bundles on nodal curves. J. Eur. Math. Soc. (JEMS) 7 (2005), no. 2, 215--251. (and earlier papers of his)